1. Field of the Invention
This invention relates to transmission and receiving of digital communications, and particularly to the generation of an orthogonal function set that makes transmission of several communication channels over an allocated frequency band possible. The orthogonal signal set is defined based on the Haar orthogonal functions in the frequency domain. The discrete version of the functions are generated by sampling and truncation the aforementioned signals. The orthogonality of the sampled and truncated signals is restored by the Singular Value Decomposition method.
2. Background of the Invention
Modulation” refers to an operation in which data is converted into a suitable form for transmission by usually carrying the data on a carrier in order to transmit information or data from one point to another point or from a first apparatus to a second apparatus through a communication line or a radio link. After received by the second apparatus, the modulated data is demodulated, that is, is restored to a suitable form to be subsequently used in the second apparatus by removing the carrier.
According to signal waves expressing information to be transmitted, such modulation includes various modulation schemes such as amplitude, frequency and time modulation schemes for a high frequency current or voltage of a sine wave, a periodic pulse or the like.
Orthogonal modulation as one of various modulation schemes is a modulation scheme using an orthogonal code in the modulation, and is characterized in that it is suitable for systems having a limitation on available power because a Signal-to-Noise Ratio (SNR) per bit required for attaining a given bit error rate goes lower as a modulation dimension increases.
Ultra-wideband (UWB) technology provides the potential for delivering a large amount of data with low power spectral density due to modulation of extremely narrow pulses. The spectrum of UWB is about 3.1 GHz to 10.6 GHz and the transmission power is low, about −41 dbm/MHz. The short duration of UWB pulses spreads their energy across a wide range of frequencies from near DC to several GHz and enables UWB signals to share the frequency spectrum with the coexisting narrowband and wideband communication systems. UWB is able to transmit broadband multimedia content over short distances, i.e. 100 feet. Although UWB communications offer a promising solution to an increasingly overcrowded frequency spectrum, sampling/truncation of digital communications destroys orthogonality.    U.S. Pat. No. 6,912,372